## Questions and Assignments to Lecture 10

10. 1. Estimate parameters of type II functional response from 2 experiments in which individual predators were kept in cages of the same size size (1 sq.m.) with different prey density for a period of 2 days.

 Number of prey per cage Number of replications Total number of prey in all cages Total number of prey killed by predators 5 20 100 35 50 5 250 60

10.2. Assume that population dynamics of spruce budworm depends mostly on generalist predators (birds) which density (P) can be considered constant in time and which have a type III functional response. The model of spruce budworm dynamics is:

where search rate (a) depends on prey density: a = bN/(N+c)

Parameter values are: r=1.5 per yr; Th = 0.0003yr; P=0.01 birds/sq.m.; b=1500 sq.m./yr; c=30 larvae/sq.m.

Find all equilibrium densities of spruce budworm population. Which equilibria are stable and which are unstable? At what population density birds fail to control spruce budworm population?

10.3. Tachinid fly Parasetigena silvestris is a parasitoid of gypsy moth. Both the host and the parasite have one generation per year. P.silvestris attacks large larvae and emerges from pre-pupae or pupae. The following results were obtained after three years of study:

 Year Density of host large larvae per sq.m. Percentage of parasitism 1988 0.45 12 1989 2.15 8 1990 4.10 ?

In 1990, parasitism was not recorded. Estimate expected percentage of parasitism in 1990 according to: 1) the model of Thompson, and 2) the model of Nicholson & Bailey. Estimate parameters of both models. Additional information: P.silvestris has a sex ration of 1:1 and pre-adult mortality of 30%.

10.4. Why the distribution of parasitoid eggs laid on hosts may be different from the Poisson distribution?

10.5. In what host-parasite models (Thompson, Nicholson & Bailey, or Rogers):

• Fecundity is limited
• Search rate is limited
• Host mortality does not depend on host density
• Host mortality does not depend on parasite density?

10.6. In what type of functional response (I, II, or III):

• Predator saturation is considered
• Predator search rate increases with prey density
• The proportion of killed prey is constant
• The proportion of killed prey first increases and then declines with increasing prey density
• The proportion of killed prey always declines with prey density?
10.7. Host density is 5 individuals per square meter; parasitoid density is 1 female per square meter; one parasitoid female can parasitize maximum 100 hosts, and its search rate (area of discovery) is 1 sq.m. per life. What is the proportion of parasitism predicted by each of three models: Thompson, Nicholson & Bailey, and Rogers?

Alexei Sharov 1/12/96